Electromagnetic radiation from a point-like charge in a weak gravitational wave: a Shapiro-delay-motivated approach

We investigate the field of a point-like electric charge freely falling in a gravitational wave. In the presence of a gravitational wave, the initially static Coulomb field of the charge becomes time-dependent and generates corresponding radiation. The gravitational wave is treated as a weak perturbation of the Minkowski metric. The electromagnetic four-potential of the charge is sought as a solution to Maxwell's equations in the gravitational wave metric, to first order in perturbation theory. The potentials of the point charge are found in quadratures throughout the space. To regularize the potentials, an approach motivated by the Shapiro effect for the time delay of radiation in a gravitational field is used. The potentials of the charge in the far zone are calculated explicitly for a monochromatic, arbitrarily polarized gravitational wave. The angular distribution of the electromagnetic radiation induced by the gravitational wave is obtained.